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Math Studies - IA

Extracts from this document...

Introduction

IB MATHEMATICAL STUDIES Internal Assessment "An investigation into the value of Ryder Cup as a reflection of the US and Europe's comparative strength in the sport of golf." Peter Frederiksen Svane St. Mary's International School IB Candidate Number: 000134 - 039 March 10th, 2008 INTRODUCTION The Ryder Cup takes place every other year in September, and is supposed to determine whether Europe or the US is the best in the sport of golf. Each side is represented by twelve golf players, who get the chance to play against each other over the course of three days. Contrary to regular tournaments, the Ryder Cup is played in a match play format1 rather than using stroke play2. The question therefore arises if the Ryder Cup is a true reflection of which region (US or Europe) has the best group of golfers. Are Europeans really better golfers than Americans, since they have won all the meets since the new millennium? To put a final answer to this debate, the investigation will focus on performances in regular tournaments, in which the Ryder Cup players have all competed, and their performance in the Ryder Cup. Various mathematical processes will be carried out within the scope of relevance in order to reach a conclusion to the mentioned task. The performance of the Ryder Cup team players in regular stroke play tournaments on their seasonal tours, where the players come in direct action against each other under the same conditions, will be determined, and this will be compared and weighed in relation to the outcome of the Ryder Cup. Hence the investigation is intended to compare the results of the Ryder Cup with the Ryder Cup players' performance in regular stroke play tournaments where they play directly against each other. Using those tournaments as the basis, it can be determined if the Ryder Cup really finds the true winner. If, for example, the European Ryder Cup players have a better score in the regular tournaments in a given period of ...read more.

Middle

= (0, 90.5) The means of X and Y equals: .995 1.713 Hence the two points on the graph can be used to find the equation of the line. First the slope is found (Rise/Run): b, which is the Y-intercept, we already have, therefore the equations is: By setting the equation equal to one, it can be found how many times bigger the US will have to lose in majors, if it is to win in the Ryder Cup. Any number below x will result in US Ryder Cup victory: (calculations on the next page). So Europe will have to perform 1.003363229 times better than US in the majors, for the US to win the Ryder Cup. Extrapolating on data, however, does not necessarily give a true prediction. So perhaps the model for the relationship between the two variables is not true. The Spearman's rank order of correlation coefficient is used to determine the strength between two sets of data. Applied in this case, it can be used to see if the results in majors agree with the results in the Ryder Cups. This measure will add another perspective in order to determine the validity of the proposed strong negative correlation. A Spearman's rank order of correlation coefficient value falls between -1 and 1. In the same as with the r-value a value of -1 is a strong negative relationship, 1 is a strong positive relationship, and as the values moves toward zero the strength of the relationship decreases. A value of zero means no correlation. The following formula is used to calculate the Spearman's rank order correlation coefficient: Where * t = Spearman's rank order correlation coefficient * d = Difference in rankings * n = Number of rankings (this value is six, since there are six data points). Summary of data A B C 2002 2003-2004 2005-2006 Majors 1.0007 .99231 .99329 Ryder Cups 1.24 1.95 1.95 d- values of the data d d A 1.0007 - 1.24 = -.2393 .05726449 B .99231 ...read more.

Conclusion

The Chi-square and application of logic, however, were coherent and thus more reliable, and therefore their conclusions were chosen. The validity of the investigation remains because the conclusions developed in a logical way, despite the limitations of the type and amount of data. ________________________________________________________________________ Word Count: 4559 APPENDICES ________________________________________________________________________ Ryder Cup players in 2002, 2004 and 2006 2002 * USA o Scott Hoch o David Toms o David Duval o Hal Sutton o Mark Calcavecchia o Stewart Cink o Scott Verplank o Paul Azinger o Jim Furyk o Davis Love III o Phil Mickelson o Tiger Woods * Europe o Colin Montgomery o Sergio Garcia o Darren Clarke o Bernhard Langer o Padraig Harrington o Thomas Bjørn o Lee Westwood o Niclas Fasth o Paul McGinley o Pierre Fulke o Phillip Price o Jesper Parnevik 2004 * USA o Tiger Woods o Phil Mickelson o Davis Love III o Jim Furyk o Kenny Perry o David Toms o Chad Campbell o Chris DiMarco o Fred Funk o Chris Riley o Jay Haas o Stewart Cink * Europe o Paul Casey o Darren Clarke o Luke Donald o Sergio Garcia o Padraig Harrington o David Howell o Miguel Angel Jimenez o Thomas Levet o Paul McGinley o Colin Montgomery o Ian Poulter o Lee Westwood 2006 * USA o Tiger Woods o Phil Mickelson o Jim Furyk o Chad Campbell o David Toms o Chris DiMarco o Vaughn Taylor o J. J. Henry o Zach Johnson o Brett Wetterich o Stewart Cink o Scott Verplank * Europe o Darren Clarke o Paul Casey o Luke Donald o Sergio Garcia o Padraig Harrington o David Howell o Robert Karlsson o Paul McGinley o Colin Montgomery o José Maria Olazabal o Henrik Stenson o Lee Westwood 1"Play in which the score is reckoned by counting the holes won by each side." 5th February, 2008: http://dictionary.reference.com/browse/match%20play> 2"Golf competition in which the total number of strokes taken is the basis of the score." 5th February, 2008: http://dictionary.reference.com/browse/stroke%20play ?? ?? ?? ?? 13 ...read more.

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